APPENDIX
The coefficients of Equation 18 are related to the coefficients of Equation 14 by the following equations: UO bi
b~ b3
= = = =
~ 1 2 z= ~ 1 3= Cz3
di d2 d3
= = = =
+ + + + + + + + +
1/3(3d B C D F) -1/3(B C 20 2F) 1/3(2B - C E - 2F) - 1 / 3 ( B - 2C 2 0 - E) - 1 / 3 ( E - 2F) - 1 / 3 ( E - 2D) 1/3E 1/3(D F ) 1/3(2D - E F) 1/3(D - E 2F)
+
+ +
The coefficients of Equation 19 can be calculated from Equation 14:
+
- 3 E 2F) 1/3(0 F ) -1/3(2D - F ) 1 / 3 ( D - 2F)
61 = 1/3(2D = fi = 71 = €1
+
+
72 =
CY% =
1/3(3A
= 7 2 = 82 = 82
€2
=
62 =
83 68 €3
=
= 73 = [3
LITERATURE CITED
(1) Beilsteins Handbuch der Organischen
for Vr2
+
+ 3C - D +
+F) 1/3(2D + E - 2F) E
= = =
7 3
+ + +
+ +
2/3(D - E 2F) 2/3(D - E 2F) 1/3(D - E - F ) -1/3(2D - 2E F) 1/3(D - E 2F)
+
ACKNOWLEDGMENT
The author thanks D. E. Ranck and C. R. Prather for carrying out the density measurements and S.G. Turley for reading the manuscript.
+ + +
1/3(3A 3B D E - F) 2/3(2D - E F) - 1 / 3 ( 2 D - E - 2F) 2/3(2D - E F) -1/3(D E - F) 1/3(2D - E F) - 1 / 3 ( D - 2E 2F)
a2 =
for V1
for
’
+
Chemie, Springer-1-erlag, Berlin, a ) Yol. 1, I1 123 (1943): b ) Yol. 1 , I11 375 (1958); c ) Yo1 2 , I11 1236 (1961). ( 2 ) Darken, L. S.,J . Am. Chem. SOC.72. 2909 (1950). ’ (3) Drucker, C., d r k i o . K e m i , 14 A, So. 15, 48 (1941 ). (4) Kortiini, G., Buchholz-lfeisenheimer, H., “Die Physik der Hochpolynieren,” T‘ol. 2 , p. 9, H. A. Stuart, ed., BpringerS’erlag, Gottingen, 1953. (5) Stull, I). Il., “Styrene, It,s Polymers, Copolymers and Ilerivatives,” p. 5 5 ) R. H. Boundy and R. F. Boyer, eds., ACP hfonograph, Reinhold, XeF York, 1952. RECEIVEDfor review March 30, 1964. Accepted >fay 18, 1963.
DissoIved Oxygen M eas u rement by Co nst a nt - PotentiaI Derivative Cou I ometry EDGAR L. ECKFELDT and E. W. SHAFFER, Jr.
R&D Cenfer, Leeds and Northrup Co., Norfh Wales, Pa.
b An experimental coulometric cell was studied, with working electrode composed of tiny metal spheres packed inside a porous ceramic tube. The cell was applied to the measurement of dissolved oxygen, and the coulometric measurements agreed with concentration va ues established by two independent methods. Good cell efficiency is attributed to the large total area of electrode surface and the thin solution layers in contact with the electrode. Possible applications include oxygen measurement of natural and industrial waters-e.g., boiler water-but field experience is needed.
C
or derivative coulometry at predetermined electrode potential and the interesting possibilities of this technique for measuring electrooxidizable or reducible substances have been‘ reported ( 3 ) . The present paper describes progress in applying the technique to the determination of dissolved oxygen in water. h new type of cell which is considerably more efficient than the one reported earlier was devised and tested over a wide range of oxygen concentration. In principle, the technique depends on introducing a sample solution at controlled flow rate into a cell where electrochemical reduction of oxygen ONTINUOUS
2008
ANALYTICAL CHEMISTRY
takes place a t an electrode of predetermined potential. The potential is selected of sufficient magnitude to effect reduction of oxygen, but is kept less than is required for reaction with the solution substrate. The electroreduction of oxygen is quantitative; each molecule of oxygen produces a current flow of 4 electrons. If properly carried out, this principle should yield a measurement of good accuracy and reliability, uninfluenced by normally troublesome variables, such as change in temperature and passage of time, because there is a direct and unalterable relat,ionship between the rate of sample oxygen influx and the cell output current, in accordance with Faraday’s law. The oxygen concentration, 5 , in normality is explicitly related to the current flow, I , in amperes and the solution flow rate, F , in litera per second, by the equation
Lv =
I ___ 96,490F
Calibration of equipment does not require the use of external oxygen standards, but instead relies on the fundamentals of the measurement, expressed by Equation 1. (A later section comments on the underlying principles, as they relate to the newly applied term “derivative coulometry.”)
Good operation of the working electrode depends on establishing conditions that will ensure the electroreduction of all oxygen inolecules in a brief interval of time. The electrode of the present study effectively achieved this objective by providing a large total surface area with only YerJ- thin solution layers in contact with it. EXPERIMENTAL
Arrangement of Equipment. The general arrangement of equipment is schematicallj illustrated in Figure 1. Sample solution from one of the sample sources entered at the bottom of the coulometric ailaly5is cell, passed through the cell inside a poious ceiaiiiic tube, and discharged through a line leading from the t o p of the cell The porous ceramic tube containpd the working electrode and qerved a. a cell diaphragm The chamber wrrounding the tube contained a second electiolyte i n nhich a secondary electrode v,as imnipi -ed Solution line> to the cell were lengths of glas. capillary tubing connected by tightly fitting ball joints .A device deqigned to inject electrolyte into the sarnllle *ohtion aaq inserted in the line leading to the cell. Thii unit rendered the sample solution basic as dealred for the coulometric reaction -\lis0 inseited was an electrolj tic oxygen generator. employed In some of the
REFERENCE ELECTRODE
SAMPLE VOLUME MEASUREMENT
COU LOMETRl C
ANALYSIS C E L
LELECTROLY TE 1 NJECTOR Figure 1.
Arrangement of equipment
work for 1)reparing solutions of known oxygen content. Incursion of atmosliheric oxygen was prevented by bubbling cylinder nitrogen w.s of prepurified grade through the olution in the outer chamber of the cell and thence through a reserve quantity of the same solution in a reservoir. Initially ,the nitrogen gas was bubbled through a water saturator. The outlet of the nitrogen line was normally kept immersed in a column of water or solution (not shown in Figure I ) and a t an adjusted height, to control the hydro,static prehsure of the secondary electrolyte inside the cell and hence its very slow rate of flow (about 0.01 ml. per minute) through the porous tube and into the sample solution. I n some cases the pressure-adjusting soliit~ioncolumn was that of t,he electrolyte injector, which arrangement allowed the single nitrogen stream to purge this solution as well. Electrical Circuit. T h e external cell circuit' (Figure 1) consisted of a n adjustable constant volt,age source, V , and a n adjustable calibrated resist'or, R1, in series. One end of this circuit was connected to the secondary electrode of the cell (lead wire 3). At the other end, the circuit was connected optionally to the first or second sections of the working electrode (lead wire 1 or 2), or to both, by means of switches !$ and Sz. The voltage source was a 10-ohm potentiometer powered by a 2-volt storage battery. A Speedomax -4ZdR recorder, MI, connected across the calibrated resistor (L&N 4750), measured the current flowing in the cell circuit. Normally, one of the lower ranges of the recorder was used (0 to 1, 0 to 2 , or 0 to 5 ma.) in conjunction with a small value of R,, thereby introducing inconsequential IR drop in the cell circuit. The potential of the working electrode was measurled by voltmeter M p (LBtN, 7664 pH meter) which was connected across the working electrode and a reference electrode (2'V silversilver chloride). The reference electrode had a small junction tube positioned in the stream of sample solution emerging from the cell.
,
Cell. T h e coulometric oxygen analysis cell is illustrated in Figure 2. T o avoid complicat'iori of t,he figure, the cell-mounting provisions and the clamping means for t h e ball joints are not shown. The cell was mounted by means of the fixtures associated with the ball joints a t its top and bottom extremities. The Kel-F end structures were firmly pressed against O-ring seals at, either end of the cell diaphragm tube by means of a spring force of 7 pounds. To ensure leakproof joints, a small amount of Dow Corning high-vacuum silicone grease was applied to the ends of the tube, and also a t all ball joints and to the O-ring seals around t,he connecting lead wires. The cell diaphragm tube was a Coors Porcelain Co. tube of Type 740 porous ceramic composition, chosen primarily because of its combination of desirable properties when filled with electrolyteonly very slow solution flow through the tube wall and good electrical conductance through the wall. The tube was X 9/32 115js inches long. Traces of an Fe+3 compound present initially in the tube material were objectionable in causing a residual cell current. Accordingly, tubes were subjected to prolonged soaking in a number of changes of dilute sulfuric acid solution. .$iter about 30 days of this treatment the rate of iron removal became very low. The sulfuric acid solution was removed from the tubes by letting dist,illed water flow through the walls. The working electrode was constructed by packing small-diameter silver metal spheres inside the cell diaphragm tube. The silver spheres ranged from 0.028 to 0.033 inch in diameter, were made of "fine silver" metal, and were obtained from the American Platinum and Silver Division of Engelhard Industries. The electrode was in two sections, separated and insulated from each other by a short packing of glass wool. The bottom section, where sample entered, was about 5 cm. long, while the upper section was almost five times this
Figure 2. Coulometric oxygen analysis cell I . Lead wire to secondary electrode 2. Upper Kel-F end structure 3. Nitrogen gas exit port 4. Buna N rubber O-rings 5. Secondary electrode, cadmium '/IO Inch dia., 3 0 inches long 6. Glass wool packing 7. Porous ceramic diaphragm tube 8. Secondary electrolyte 9. Nitrogen gas inlet port IO. Lower Kel-F end structure 1 I . Sample solution inlet port 12. Sample solution outlet port 13. Lead wire to second section of working electrode 14. O-ring sealing nut 15. Secondary electrolyte inlet (plan, item 9 ) 16. Second section of working electrode 17. Cell casing, borosilicate glass pipe, 1 inch I.D. 18. First section of working electrode 19. Kel-F inlet tube for secondary electrolyte 20. Silver tubing conductor t a first section of working electrode 21. Leadwire to silver tubing conductor
+
length. Measurements on dummy cells indicated that electrical conduction was satisfactory a t the points of contact between adjacent spheres throughout the packing and between the packing and leadout conductors. Calculation indicates that the packed sphere electrode of the present cell provided a geometrical surface area of about 25 sq. cm. per linear centimeter of column length. Thus the first section of the working electrode presented about 125 sq. em. total area, while the second section presented an estimated 600 sq. cm. of area. Additionally, the interstices were of small dimensions. Calculation indicates that the most remote point of the solution filling the interstices was not more than about 0.06 mm. from a n element of the electrode surface. These factors favored the rapid and quantitative electrochemical reduction of the osygen of the incoming sample solution. Furthermore, the VOL 3 6 , NO. IO, SEPTEMBER 1 9 6 4
2009
Figure 3. Potassium carbonate electrolyte injector
packed column electrode did not significantly impede the flow of solution through it. The secondary electrode of cadmium wire in the form of an open wound helix presented to the solution a calculated geometric area of about 50 sq. cm. This electrode was immersed in a 2M potassium chloride solution which comprised the secondary electrolyte. When the cell was in operation, this solution was kept free of oxygen as stated. Needed make-up solution was automatically drawn from the reservior. Substrate Effects. Preliminary work had indicated t h a t pure water and potassium chloride solutions were not satisfactory for making lorn-level oxygen measurements. Basic conditions as produced by potassium carbonate or hydroxide were preferred. Because of greater ease of handling, the carbonate was selected for injection into the sample solution. This objective was accomplished automatically with the device illustrated in Figure 3. h concentrated potassium carbonate solution, kept purged of oxygen by flow of nitrogen gas, passed through the frit of the device a t a rate of about 0.01 ml. per minute and entered the sample line. With the injector in operation, the sample stream was held within pH limits of 10.6 and 11.1. Air- and Oxygen-Saturated Solutions. Air-baturated water was used not only directly in some of the tests but also in making u p samples of low oxygen content by a dilution technique. .\ survey of the literature revealed a number of references giving concordant oxygen Concentration values for air-saturated water ( 1 , 2, 5-10). Theie values mere averaged to obtain 2010
e
ANALYTICAL CHEMISTRY
the figure used in the work--8.27 mg. of oxygen per liter of soluticn a t 25' C. and 760-mm. total pressure. I n obtaining and applying this figure, corrections when needed were made for variations from standard pressure and 2.5' C. using Henry's law and the relationship for concentration change with temperature given in one of the sources ( 5 ) . Oxygen-saturated solutions were made by bubbling Airco cylinder oxygen through distilled water. Oxygen concentration values were obtained from air-saturated values a t corresponding pressure and temperature by multiplying by the oxygen percentage ratio, 100/20.99. Oxygen-Free Solutions. Oxygenfree.water was prepared in two ways: by simply bubbling nitrogen gas -of prepurified grade through distilled water for a period of time; and by withdrawing a stream of liquid from a volume of boiling distilled water, the surface of which was protected by a blanket of nitrogen gas or by a current of escaping steam. Because the two methods gave comparable results, the simpler, nitrogen purging, was used in most of the .work. Precautions were taken to ensure t h a t the starting distilled water did not contain traces of a nonvolatile oxid a n t t h a t would respond like oxygen in the coulometric measurement cell. Solution Preparation by Dilution. Most of the oxygen samples were prepared in 'a special apparatus which was designed t o permit a known volume of air-saturated water to be added to a known volume of oxygenfree water, under conditions which prevented accidental loss or gain of oxygen. T h e apparatus, which was constructed of borosilicate glass, is illustrated in Figure 4.
To use the apparatus, plunger C with its stopper was removed, and distilled water or solution was added to the flasks until the upper flask was two thirds full. With the plunger replaced and in raised position 1, the Kel-F tube, B, was lowered to the bottom of the lower flask, and nitrogen gas (prepurified grade) was bubbled through the liquid in both flasks until all oxygen was purged. With nitrogen still flowing, tube B was raised to discharge into the upper flask, A , and plunger C was lowered to position 2 . Stirrer F was now turned on, and a measured amount of air-saturated water was slowly added to flask E through stopcock J from the graduated tube, K . After this operation was completed, oxygen transfer to or from the solution was prevented by the plunger acting as a barrier. The only slight communication to the upper part of the apparatus was furnished by the waterfilled annulus of capillary dimensions, formed by the plunger fitting closely within the connecting tube, D.
(NITROGEN
LINE)
C-PLUNGER POSITION I PQSlTlON 2 0-CONNECTING TUBE
F- MAGNETIC STIRRING BAR
Figure 4. tus
Volumetric dilution appara-
The temperature of the air-saturated water used for the dilution was noted and corrected for, but no barometric pressure correction was introduced in this phase of the work. I t was thought that errors of the dilution procedure would be greater than any errors arising from pressure variations. The concentration of oxygen in flask E was obtained by calculation. If one assumes perfect mixing, the following differential equation applies V p
dc = ( X
- C ) du
(2)
The equation takes into account the oxygen which both entered and left flask E a t the time the air-saturated water was admitted. Integration of Equation 2 from 0 to C, and 0 to VI gives the equation used
where
C
=
X
=
Ti, =
Vz
=
dissolved oxygen concentration in flask E , mg. per liter p.p.m. dissolved oxygen concentration of air-saturated water added, p.p.m. volume of air-saturated water added, liters volume of flask E (3.16 liters)
During a test, the solution of known oxygen concentration in flask E passed through stopcock H and entered the sample line leading to the coulometric cell. When sample was thus withdrawn, oxygen-free water entered from the upper chamber, passing through the narrow annulus. The amounts of water taken for a test and hence the amount of oxygen-free water entering
PLATlNUM ELECTRODES-
were sufficiently small to introduce only a negligible decrease in oxygen concentration of the solution in flask E .
-I
,
assumed by the cadmium secondary electrode (about -0.85 volt). The adjustable voltage source thus was used to introduce into the circuit only about 0.05 volt. Oxygen Measurements. An objective of the work was to compare actual cell performance in measuring known concentrations of dissolved oxygen, with the theoretical requisites of Equation 1.
BOROSILICATE GLASS CAP1 LLARY TUBING-7
/
TERMINAL-#
5mm BORE
/
--&S
+ 4 H20
VOL. 36, NO. 10, SEPTEMBER 1964
2013
